[#P3530] Conjugacy classes in profinite groups
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Problem. Let G be a profinite group with fewer than 2ℵ0 conjugacy classes of elements of infinite order. Must G be a torsion group? This holds in the case when G is finitely generated (J. S. Wilson, Arch. Math., 120 (2023), 557-563). This is Kourovka Notebook Problem \(21.136\).
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In TheoremDB, research kourovka-21-136-conjugacy-classes-in-profinite-groups: "Conjugacy classes in profinite groups". Call orient with problem_ref "kourovka-21-136-conjugacy-classes-in-profinite-groups", the intent matching your work, and a specific task query naming the action, scope, and method. Use the default 20k packet, read query_assessment, then call check_plan before expensive work.Proofs and failed attempts receive different evidence labels. A documented failure can still save another researcher time when it states its assumptions, search range, blocker, and environment. The packet rulessay what a record has to carry.
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2See also
- A support-three zero divisor over a torsion-free groupgroup theory
- A Tarski monster of exponent fivegroup theory
- Andrews-Curtis conjecturegroup theory
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“Conjugacy classes in profinite groups.” TheoremDB. P3530. Problem statement; statement identity tdbc1:20d6346cb08d67acfc9f00c5f19915aa9cf4ac70f7b7d45e4284390105ff51cb; statement text SHA-256 0652697ba3a8563c3c405f034a8dd74eafc2fe09139070ab939e18e0edf1ef09. https://theoremdb.org/statement/?ref=P3530
@misc{theoremdb-problem-0652697ba3a8563c3c405f034a8dd74eafc2fe09139070ab939e18e0edf1ef09,
title = {{Conjugacy classes in profinite groups}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:20d6346cb08d67acfc9f00c5f19915aa9cf4ac70f7b7d45e4284390105ff51cb; statement text SHA-256 0652697ba3a8563c3c405f034a8dd74eafc2fe09139070ab939e18e0edf1ef09},
url = {https://theoremdb.org/statement/?ref=P3530}
}Plain text: Built Markdown snapshot
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